Parallel composition of logic calculi with proofs as generalized 2-cells
نویسندگان
چکیده
Recent graph-theoretic developments [26, 27] in the semantic theory of combination of logics look at a signature as a multi-graph (of sorts and connectives) and obtain the induced language as the category of multipaths where formulas appear as morphisms. This idea is carried over to Hilbert-style deductive systems by looking at an inference rule as a metaedge from its premises to its conclusion. From such a deductive system, a generalized 2-category is induced where proofs appear as 2-cells. Vertical composition is used for concatenating proofs and horizontal composition for instantiation. The workability of the approach is illustrated by defining free and synchronized variants of parallel composition of deductive systems and proving the conservative nature of the free variant.
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